4 The Analysis
4.2 The procedure
This is a practical analysis of finding the flowrate as a function of pressure drop. Upstream choke pressure and downstream choke pressure will determine the pressure drop across a choke. By making some simplifications and using Bernoulli principle associated with increase of flow speed, a calculated flowrate through choke is conducted.
In this work there will be performed analysis on the wells M-01 to M-15 on the Ekofisk 2/4 Mike platform, except for M-08 and M-13 which was sidetracked during the period of research. M-07 has a continuous slug flow.
Analyzing the behavior of real time estimated production will be performed in the following way:
1. Use temperature as a verification of real-time estimated production
2. Calculate flow rates from Bernoulli’s equation, and use pressure drop across chokes.
3. If thereal-time estimated production becomes unverified, the well model will be tuned against Bernoulli flowrates and implemented in the network model for new simulations and checked for temperature verification.
4.2.1 The Pressure Ratio
The pressure ratio is a ratio of the downstream pressure relative to the upstream pressure.
4.2.2 A Temperature Verification
Results of the WellFlo’s calculated flow rate provide a corresponding calculated wellhead temperature and pressure. The calculated temperature will be used as a production verification status, by compare the calculated temperature with the measured wellhead temperature. Accepted deviation in measured temperature is set by a upper and lower limit of the calculated temperature.
34 An alarm will be trigged when the measured temperature is crossing the limit. This deviation will be an indication of that there has been a change in the wells performance. The estimated production is no longer representing the welltest due to changes in flowrate, watercut, GOR, etc.
It is of importance to be aware of that the estimated flowrates is controlled by the vertical lift performance curve (VLP) and not the inflow performance cure (IPR). The shape of the IPR curve, calculated in WellFlo, will only be changed by variations in water cut or GOR, while a change in the liquid rate (or reservoir pressure) will translate the VLP. This means that the estimated flowrates is only controlled by the pressure drop in the tube. This is shown by the step wise estimates following the welltests, see fig [4.1]
In this analysis the temperature verification primarily is used as a helping tool to find a more
meticulous way of measuring the “natural” decline in production rate between well tests. The aim is to bring a smoother curve in the production rate versus time, instead of the step wise production estimates.
Figure 4.1. The figure is showing the RT-estimated production become unverified. The blue line represents how the Bernoulli equitation can be used and implemented in the well model in order to verify the estimates.
The upper and lower temperature limit was at first fixed to 20 degrees Fahrenheit. This seemed to be to large accepted deviation for some wells, resulting in a too high number of verified normal
producing wells. Some temperature limits were reduced to 5 degrees Fahrenheit, which seems to be a good tolerance in accepted deviation for temperature. For gas lifted, slugging or unstable wells the tolerance has to be greater due to more various temperatures. For these wells the limit is 10 degrees Fahrenheit.
The Temperature Verification is directly connected to Optimum Online’s real-time estimations. The system will trig an alarm when a well is unverified, (see appendix A).
4.2.3 Pressure Drop Measurements Across Choke
For unverified production, the next step is to use the surface data and make new references in the network model to improve estimated production in Optimum Online, and also by using the new data sources in determining changes that may have occurred in the well performance. This can be
35 achieved by using Bernoulli’s principle and pressure drop across the choke. Bernoulli’s principle is described in section (2.10).
Measurements of upstream choke pressure and downstream choke pressure are retrieved from PI.
Before calculations, some theoretical assumptions have to be made:
- Incompressible liquid rate
- Constant mixture density (between the well tests or until change in choke size).
- Constant error from transmitter data.
Flow characteristics through the choke can be difficult to predict as one may have to assume slip in the flow regime, the moment a flow is passing through the choke. Simultaneously changes in densities varying with the pressure upwards the tube makes it difficult to predict a representative value of the mixture density. Variations in the velocities also will influence the value of the discharge coefficient and must be considered when using Bernoulli’s principle. Another important
consideration is to allow changes in choke size that will immediately change all these parameters. It can be difficult to maintain a sufficient complete overview of the uncertainties in the modeling process.
First, considering the available information:
- Individual flowrates from well tests - Duration of well tests
- Pressure drop across the choke - Monitoring the choke size.
4.2.4 Discharge Coefficient
When using the Bernoulli’s principle to calculate a flowrate through choke, there is some extra pressure losses which must be compensated. These may be put into a discharge coefficient Cd which account for additional flow effects.
The discharge coefficient is a function of the Reynolds number and varies a lot in multiphase flow.
Well tests measurements at test separator on the 2/4 Mike platform has showed a variation of the discharge coefficient from 0.91 to 0.96. Other measurements showed uncertainties of the CD up to 20%., [10].
Different methods for calculations of the discharge coefficient are published with varying results, refer to [2] for further information. Determination of a good discharge estimator depends on finding a dependency of CD in combination of many variables in terms of physical geometry and mixture properties.
Now considering eq. (2.31) Bernoulli and introduce a discharge coefficient CD, to compensate for the friction loss:
(4.1)
36 The dimensionless constant KV is calculated from the cross sectional areas before and at the
restriction (choke). Variations in the choke size will result in a calculation of a new constant (Kv) Also, it has to be considered the risk of scale formation in the choke, and thereby incorrect choke size. A change in the choke size will also influence the fluid properties as density and flow regime.
By averaging the pressure drop during the welltest, it will be representative to the flowrate at welltest. (read section 2.4.1 for more details on performing the welltest). Equation (3.4) may now be reversed with respect to KV:
(4.2)
Where
QWT - is the average of the mixed flowrate during the welltest
∆pkv - is the averaged pressure drop during welltest Ρm - is the mixture density
Cd - is the discharge coefficient
The KV value is calculated by not using the cross sectional areas due to choke variables settings and the risk of scale that also may influence the diameter. Instead it is determined during welltest. Now the flowrate can be calculated by equation (3.4):
(4.3)
Where
∆pcurrent - is the current pressure drop
And by replacing KV:
(4.5)
As can be seen by eq.(3.5), the calculated rate depends mainly on correct estimation of the density and discharge coefficient. As mentioned previous, these parameters varies a lot and involves
37 uncertainties. The model has to be simplified, due to the lack of simultaneous gas-liquid-ratio
measurements:
- The mixture density is kept constant between the welltests or until a change in the choke size.
- The discharge coefficient is kept constant until a new welltest or change in the choke size.
Now the calculated flowrate can be expressed as a function of pressure drop:
(4.6)
During the welltest, the ∆pcurrent also should be averaged so that QV is equal to QWT in order do get a fully representative estimate of the rate as a function of the pressure drop. From the moment a welltest is over, the current pressure drop (∆pcurrent) will vary and ∆pKV remains constant until new calculations when a new welltest is performed or there has been a change in the choke size.
The calculated flowrate does not split the phases and is preliminary a measurements of total flow rate. An alternative is to use the single flowrates from welltest. This method does not account for changes in watercut and GOR. The calculated flowrate will be compared with the total estimated production from Optimum Online.
4.2.5 Building the flow rate model
To qualify the KV, new calculations have to be done while monitoring:
- New welltests - Change in choke size
- dP the moment Kv is calculated.
These parameters are the most important for calibratinging KV in certain intervals. Also, the calculation account s for the uncertainties in densities and discharge coefficients. Figure 4.2 is showing an influence diagram of the dependencies in the process.
Monitoring
Calculate
Qv
Establish
new Kv
38 Figure 4.2. Influence diagram showing the dependencies in calculations. Qv is the Bernoulli flowrate.
Calculations of the new flowrate, QV may be done continuously, varying with the pressuredrop measurements. The resolution in time are optional from PI. A high time resolution will be able to detect slugging in the wells, which can be a problem in some wells on the Ekofisk Field.
4.2.6 The mixture density
The mixture density must be converted to upstream condition:
The mixture density, ρm are calculated from the individual flowrates taken from welltests and PVT reports.. The liquid phase is assumed incompressible and gas is converted to upstream conditions by determining the compressibility factor.